Can someone help me with this?

1) |a+b| </= (Lesser than or equal to) |a| + |b|

I tried for some time, but I cant get this... :S

For the next few I have to find the solution sets for x

2) 4 - |x| > |2x|

3) |x/3 - 1| > |x|

The concept of the modulus signs is new to me, and hence I'd appreciate if someone could do the above sums as example sums so I could complete the homework on my own as well as prepare for the test on monday

Yup, but I got +4/3 -4/3 >.<

I got where I made the mistake.

Could anyone help me with the others please?

Especially 1) |a+b| < Or = |a| + |b|



I was getting really worked up about the third one because in 3) For case 1 where we take x to be +ve, i got a -ve answer, and vice versa, I thought I was doing it wrong

I just did the whole working and wrote not possible
|a+b| < = |a| + |b|

it's called the triangle inequality |a| and |b| are the two adjacent sides of the triangle |a+b| is the third side. Logically, |a+b| is bigger than |a| and |b| but is either < or = to |a|+|b|
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